| test | aim | variable | p_value | alpha_value | Decision |
|---|---|---|---|---|---|
| Shapiro-Wilk test | Normality | residuals | 0.5176650 | 0.05 | Ho no rejected |
| Bartlett test | Homogeneity | residuals | 0.0150452 | 0.05 | Ho Rejected |
| Anova 1 way | Mean | mpg | 0.0000000 | 0.05 | Ho Rejected |
Anova 1 Way - Fixed Model - General Linear Models
Report - Anova 1 Way - Fixed Model - General Linear Models
1) Anova test
Rscience - AI Report (Auto Report)
The null hypothesis of normal distribution of residuals is not rejected.
The hypothesis of homogeneity of variances (homoscedasticity) is rejected.
Not all model assumptions are met, so it is NOT valid to draw conclusions from the ANOVA test.
Regardless of the p-value obtained in ANOVA, it is not valid to draw conclusions.
1) References
$df_selected_vars
order var_name var_number var_letter var_role doble_reference
1 1 mpg 1 A VR VR(mpg)
2 2 cyl 2 B FACTOR FACTOR(cyl)2) Summary Factor
$df_factor_info
order level n mean color
1 1 4 11 26.66364 #FF0000
2 2 6 7 19.74286 #00FF00
3 3 8 14 15.10000 #0000FF
$check_unbalanced_reps
[1] TRUE
$phrase_selected_check_unbalanced
[1] "The design is unbalanced in repetitions. A correction is applied to the Tukey test."3) Anova 1 way - Table
$df_table_anova
Df Sum Sq Mean Sq F value Pr(>F)
FACTOR 2 824.7846 412.39230 39.69752 4.978919e-09
Residuals 29 301.2626 10.38837 NA NA4) Multiple comparation test (Tukey)
$df_tukey_table
level mean group
1 4 26.66364 a
2 6 19.74286 b
3 8 15.10000 c5) Model Error
$df_model_error
order level n model_error_var_MSE model_error_sd model_error_se raw_error_se
1 1 4 11 10.38837 3.223099 0.9718008 0.9718008
2 2 6 7 10.38837 3.223099 1.2182168 1.2182168
3 3 8 14 10.38837 3.223099 0.8614094 0.86140941) Requeriment - Normaility test - Residuals
$test_residuals_normality
Shapiro-Wilk normality test
data: minibase_mod$residuals
W = 0.97065, p-value = 0.51772) Requeriment - Homogeneity test - Residuals
$test_residuals_homogeneity
Bartlett test of homogeneity of variances
data: residuals by FACTOR
Bartlett's K-squared = 8.3934, df = 2, p-value = 0.015053) Estimated variances - Residuals
$df_model_error
order level n model_error_var_MSE model_error_sd model_error_se raw_error_se
1 1 4 11 10.38837 3.223099 0.9718008 0.9718008
2 2 6 7 10.38837 3.223099 1.2182168 1.2182168
3 3 8 14 10.38837 3.223099 0.8614094 0.8614094
$df_raw_error
order level n raw_error_var raw_error_sd
1 1 4 11 20.338545 4.509828
2 2 6 7 2.112857 1.453567
3 3 8 14 6.553846 2.560048
$phrase_info_errors
[1] "Anova and Tukey use MSE from model."
[2] "Bartlett use variance from raw error on each level."
[3] "Only if there is homogeneity from raw error variances then is a good idea take desition from MSE."$df_table_factor_plot001
order level n mean min max sd var
4 1 4 11 26.66364 21.4 33.9 4.509828 20.338545
6 2 6 7 19.74286 17.8 21.4 1.453567 2.112857
8 3 8 14 15.10000 10.4 19.2 2.560048 6.553846$df_table_factor_plot002
order level n mean model_error_sd lower_limit upper_limmit color
4 1 4 11 26.66364 3.223099 23.44054 29.88674 #FF0000
6 2 6 7 19.74286 3.223099 16.51976 22.96596 #00FF00
8 3 8 14 15.10000 3.223099 11.87690 18.32310 #0000FF$df_table_factor_plot003
order level n mean model_error_se lower_limit upper_limmit color
4 1 4 11 26.66364 0.9718008 25.69184 27.63544 #FF0000
6 2 6 7 19.74286 1.2182168 18.52464 20.96107 #00FF00
8 3 8 14 15.10000 0.8614094 14.23859 15.96141 #0000FF$df_table_factor_plot004
order level min mean Q1 median Q3 max n color
4 1 4 21.4 26.66364 22.80 26.0 30.40 33.9 11 #FF0000
6 2 6 17.8 19.74286 18.65 19.7 21.00 21.4 7 #00FF00
8 3 8 10.4 15.10000 14.40 15.2 16.25 19.2 14 #0000FF$df_table_factor_plot005
order level min mean Q1 median Q3 max n color
4 1 4 21.4 26.66364 22.80 26.0 30.40 33.9 11 #FF0000
6 2 6 17.8 19.74286 18.65 19.7 21.00 21.4 7 #00FF00
8 3 8 10.4 15.10000 14.40 15.2 16.25 19.2 14 #0000FF$df_table_factor_plot006
order level min mean Q1 median Q3 max n color
4 1 4 21.4 26.66364 22.80 26.0 30.40 33.9 11 #FF0000
6 2 6 17.8 19.74286 18.65 19.7 21.00 21.4 7 #00FF00
8 3 8 10.4 15.10000 14.40 15.2 16.25 19.2 14 #0000FF$df_table_factor_plot007
order level n mean model_error_se lower_limit upper_limmit color group
4 1 4 11 26.66364 0.9718008 25.69184 27.63544 #FF0000 a
6 2 6 7 19.74286 1.2182168 18.52464 20.96107 #00FF00 b
8 3 8 14 15.10000 0.8614094 14.23859 15.96141 #0000FF c$df_table_residuals_plot001
order level n min mean max var sd color
4 1 4 11 -5.263636 -4.037175e-17 7.236364 20.338545 4.509828 #FF0000
6 2 6 7 -1.942857 -7.943233e-18 1.657143 2.112857 1.453567 #00FF00
8 3 8 14 -4.700000 1.193252e-17 4.100000 6.553846 2.560048 #0000FF$df_table_residuals_plot002
order level n min mean max var sd color
4 1 4 11 -5.263636 -4.037175e-17 7.236364 20.338545 4.509828 #FF0000
6 2 6 7 -1.942857 -7.943233e-18 1.657143 2.112857 1.453567 #00FF00
8 3 8 14 -4.700000 1.193252e-17 4.100000 6.553846 2.560048 #0000FF$df_table_residuals_plot003
order level n min mean max var sd color
4 1 4 11 -5.263636 -4.037175e-17 7.236364 20.338545 4.509828 #FF0000
6 2 6 7 -1.942857 -7.943233e-18 1.657143 2.112857 1.453567 #00FF00
8 3 8 14 -4.700000 1.193252e-17 4.100000 6.553846 2.560048 #0000FF$df_table_residuals_plot004
variable n min mean max var sd
1 residuals 32 -5.263636 -1.040834e-17 7.236364 9.718148 3.117394
model_error_var_MSE model_error_sd
1 10.38837 3.223099$df_table_residuals_plot005
variable n min mean max var sd
1 residuals 32 -5.263636 -1.040834e-17 7.236364 9.718148 3.117394
model_error_var_MSE model_error_sd
1 10.38837 3.223099$df_table_residuals_plot006
order level n min mean max var sd color
4 1 4 11 -1.6330981 -2.020559e-17 2.2451573 1.9578196 1.3992211 #FF0000
6 2 6 7 -0.6027917 -2.723816e-18 0.5141459 0.2033869 0.4509843 #00FF00
8 3 8 14 -1.4582240 -1.256150e-18 1.2720678 0.6308833 0.7942816 #0000FF$df_table_residuals_plot007
order level n min mean max var sd color
4 1 4 11 -1.6330981 -2.020559e-17 2.2451573 1.9578196 1.3992211 #FF0000
6 2 6 7 -0.6027917 -2.723816e-18 0.5141459 0.2033869 0.4509843 #00FF00
8 3 8 14 -1.4582240 -1.256150e-18 1.2720678 0.6308833 0.7942816 #0000FF$df_table_residuals_plot008
variable n min mean max var sd
1 studres 32 -1.633098 -8.104411e-18 2.245157 0.9354839 0.9672042$df_table_residuals_plot009
variable n min mean max var sd
1 studres 32 -1.633098 -8.104411e-18 2.245157 0.9354839 0.9672042$df_table_residuals_plot010
variable n min mean max var sd
1 studres 32 -1.633098 -8.104411e-18 2.245157 0.9354839 0.96720421) Summary Anova 1 way
$df_summary_anova
test aim variable p_value alpha_value
1 Shapiro-Wilk test Normality residuals 5.176650e-01 0.05
2 Bartlett test Homogeneity residuals 1.504518e-02 0.05
3 Anova 1 way Mean mpg 4.978919e-09 0.05
Decision
1 Ho no rejected
2 Ho Rejected
3 Ho Rejected
$phrase_shapiro_selected
[1] "The null hypothesis of normal distribution of residuals is not rejected."
$phrase_bartlett_selected
[1] "The hypothesis of homogeneity of variances (homoscedasticity) is rejected."
$phrase_requeriments_selected
[1] "Not all model assumptions are met, so it is NOT valid to draw conclusions from the ANOVA test."
$phrase_anova_selected
[1] "Regardless of the p-value obtained in ANOVA, it is not valid to draw conclusions."2) Tukey
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